A good base

where are you now?

We are in Oxford until Thursday.

Reading is very well connected by train (and from Oxford), and convenient to Heathrow if that where you need to be in 5 days. You may find a hotel at a better price than in Cambridge.

Then again it would be such a shame to miss Cambridge and maybe your foot will feel better soon.

I stayed in Staines Aug 23-26 2023. It's southwest of Heathrow T5 terminal (about a 20-25 min cab ride). There's a Premier Inn there but I stayed at a different hotel nearer to the Thames River. The Premier Inn is closer to the rail station. Where I stayed was about a 20 min walk to the rail station, which the more times that I did it, I found shorter and more pleasant ways to walk (through a city park on the last day).

Not sure if 'good rail access' means no changes from one train line to a different one. I traveled from Staines via Reading to Newbury (for Highclere Castle visit) and via Clapham Junction to London Victoria station (for Buckingham Palace visit).

I wanted to visit Runnymede (Magna Carta memorial) and the Air Forces Memorial, however it didn't work out while I was there. I hope to visit Staines in future in order to see these memorials.

EDIT to add: Staines is also on a bus route from Heathrow, which I didn't initially mention since you might not want to travel via bus with a twisted ankle.

Staines might fit your 'quiet town on a rail line' with a few things to see. I didn't check on current hotel prices however.

If you're booked on the train to Cambridge anyway I might be tempted to extend the ticket to the end of the line at Kings Lynn.
A pretty flat and compact town, very nice architecturally.

Should be cheaper prices but if you feel like it Cambridge and Ely are still easy to access. As are the North Norfolk beaches.

I'm just concerned about the changes of train to get there.I

That is where Somewhere like Reading might be better.

Henley is two changes of train, but Maidenhead would be just one change, at Reading.